Question 1; Grain growth in metals basically follows the same principles or reaction kinetics as diffusion, where grain size is proportional to the square root of time * a grain growth coefficient. This grain growth coefficient is similar to a diffusivity coefficient, which is proportional to temperature. So, the higher the temperature for the same amount of time, results in grain growth.
Question 2; Referring to the iron-carbon phase diagram, the solubility of carbon increases as a function of increasing temperature. This is due to the ability of the austenite phase, which is a face centered cubic structure, to accommodate more carbon atoms at higher temperature. Also, the diffusivity of carbon atoms is much higher than other elements, so carbon atoms can rapidly enter and dissolve in austenite.
Question 3; Carbon is an austenite former, so as the carbon content increases, the ability to retain austenite increases at lower temperatures. The retained austenite is what reduces hardness.
Quench cracks are normally formed under conditions where the surface of a part cools more rapidly than the core. For example, if we take a steel bar (like an AISI Type 1080) and quench in water, the outer region of the bar will immediately transform to martensite. While the bar is still cooling, the core of the bar begins to transform to other phases at lower temperatures. During the formation of these other phases in the core, transformation stresses are produced because of differences in volume between the martensite and the other phases. If the martensite is too brittle and can't accommodate the transformation stresses from the core, the martensite will either deform or crack. Because carbon effects the hardness of martensite (as carbon content increases the hardness of martensite also increases), higher carbon alloys will generally have a greater tendency to develop quench cracks. This is the reason why certain alloying elements are added to steels to slow down the rate of phase transformation (lower the tranformation temperature), enabling the outer surface and core of the bar to transform together.